Trees and the Kurepa hypothesis for left factorial

Aleksandar Petojević, Mališa Žižović

We construct certain trees. From tlreir properties we establish the connections between $!n$ and $n!$. We give a necessary and sufficient condition for primality of a number and two equivalents of Kurepa's hypothesis for left factorial also. We define a sequence $D_i(n)$ and another equivalent of Kurepa's hypothesis based on proporties of this sequence.